Download K2-98b: A 32 M ⊕ Neptune-Siza Planet in a 10 Day Orbit Transiting

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K2-98 b: A 32-M⊕ NEPTUNE-SIZED PLANET IN A 10-DAY ORBIT TRANSITING AN F8 STAR
arXiv:1608.01165v2 [astro-ph.EP] 7 Oct 2016
Oscar Barragán1 , Sascha Grziwa2 , Davide Gandolfi1,3 , Malcolm Fridlund4,5 , Michael Endl6 , Hans J. Deeg7,8 ,
Manuel P. Cagigal9 , Antonino F. Lanza10 , Pier G. Prada Moroni11,12 , Alexis M. S. Smith13 , Judith Korth2 ,
Megan Bedell14 , Juan Cabrera13 , William D. Cochran6 , Felice Cusano15 , Szilard Csizmadia13 ,
Philipp Eigmüller13 , Anders Erikson13 , Eike W. Guenther16 , Artie P. Hatzes16 , David Nespral7,8 ,
Martin Pätzold2 , Jorge Prieto-Arranz7,8 , and Heike Rauer13,17
1
Dipartimento di Fisica, Università di Torino, via P. Giuria 1, 10125 Torino, Italy; [email protected]
2
Rheinisches Institut für Umweltforschung an der Universität zu Köln, Aachener Strasse 209, 50931 Köln, Germany
3
Landessternwarte Königstuhl, Zentrum für Astronomie der Universität Heidelberg, Königstuhl 12, 69117 Heidelberg, Germany
4
Leiden Observatory, University of Leiden, PO Box 9513, 2300 RA, Leiden, The Netherlands
5
Department of Earth and Space Sciences, Chalmers University of Technology, Onsala Space Observatory, 439 92 Onsala, Sweden
6
Department of Astronomy and McDonald Observatory, University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712,
USA
7
Instituto de Astrofı́sica de Canarias, 38205 La Laguna, Tenerife, Spain
8
Departamento de Astrofı́sica, Universidad de La Laguna, 38206 La Laguna, Spain
9
Departamento de Fı́sica Aplicada, Universidad de Cantabria Avenida de los Castros s/n, E-39005 Santander, Spain
10
INAF - Osservatorio Astrofisico di Catania, via S. Sofia 78, 95123, Catania, Italy
11
Physics Department ”E. Fermi”, University of Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy
12
Istituto Nazionale di Fisica Nucleare, Largo B. Pontecorvo 3, 56127, Pisa, Italy
13
Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse 2, 12489 Berlin, Germany
14
Department of Astronomy and Astrophysics, University of Chicago, 5640 S. Ellis Ave, Chicago, IL 60637, USA
15
INAF Osservatorio Astronomico di Bologna, Via Ranzani, 1, 40127, Bologna
16
Thüringer Landessternwarte Tautenburg, Sternwarte 5, D-07778 Tautenberg, Germany
17
Center for Astronomy and Astrophysics, TU Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
ABSTRACT
We report the discovery of K2-98 b (EPIC 211391664 b), a transiting Neptune-sized planet monitored
by the K2 mission during its campaign 5. We combine the K2 time-series data with ground-based
photometric and spectroscopic follow-up observations to confirm the planetary nature of the object
and derive its mass, radius, and orbital parameters. K2-98 b is a warm Neptune-like planet in a 10-day
orbit around a V=12.2 mag F-type star with M? =1.074 ± 0.042 M , R? =1.311+0.083
−0.048 R , and age
of 5.2+1.2
Gyr.
We
derive
a
planetary
mass
and
radius
of
M
=
32.2
±
8.1
M
and
Rp =4.3+0.3
p
⊕
−1.0
−0.2 R⊕ .
K2-98 b joins the relatively small group of Neptune-sized planets whose both mass and radius have
been derived with a precision better than 25 %. We estimate that the planet will be engulfed by its
host star in ∼3 Gyr, due to the evolution of the latter towards the red giant branch.
Keywords: planets and satellites: detection — planets and satellites: individual: K2-98 b
(EPIC 211391664 b) — stars: fundamental parameters
1. INTRODUCTION
The transit of an exoplanet in front of its host star
provides us with valuable information about its size.
When combined with radial velocity (RV) measurements
(e.g., Mayor & Queloz 1995) or transit timing variations
(TTVs, e.g., Ford et al. 2011), transit photometry gives
us access to the geometry of the orbit, enabling the measurement of the true mass of the planet, of its radius,
and consequently of its mean density. Masses, radii,
densities, and orbital parameters are fundamental “in-
gredients” to study the internal structure, composition,
dynamical evolution, tidal interaction, architecture, and
atmosphere of exoplanets (e.g., Winn & Fabrycky 2015;
Hatzes 2016).
The space-based photometry revolution of CoRoT
(Baglin et al. 2006) and Kepler (Borucki et al. 2010)
has given us access to the small-radius planet domain (Rp . 6 R⊕ , i.e., Neptune- and Earth-sized planets), a regime that is not easily accessible from
the ground. Neptune-like planets (2.0 . Rp . 6.0 R⊕ ,
2
Barragán et al.
10 . Mp . 40 M⊕ Borucki et al. 2011) are of special interest as they mark the transition from Super-Earths to
larger planets with higher volatile content, more akin to
the icy giants in our solar system. However, our knowledge of these planets is still quite limited. Although
Kepler has found that ∼26 % of Sun-like stars in our
Galaxy host small planets with orbital period shorter
than 100 days (Marcy et al. 2014), determinations of
masses with a precision of ∼25 % – or better – have
been possible only for a few dozen Neptune-like planets1 . This is because of the small RV variations induced
by such planets and the faintness of most of the Kepler
host stars (V>13 mag), which makes them not suitable
for precise RV follow-up observations.
In its extended K2 mission, Kepler is surveying different stellar fields located along the ecliptic, performing 80-day-long continuous observations of 10 000–20 000
stars per campaign. K2 data products have no proprietary period and are released to the community typically three months after the end of each campaign, enabling immediate follow-up observations. The K2 mission is an unique opportunity to gain knowledge of transiting Neptune-sized planets (e.g., Espinoza et al. 2016;
David et al. 2016). K2 is targeting a number of bright
dwarfs (V≤12 mag) higher than the original Kepler mission (Howell et al. 2014). This is a definitive advantage
for any RV follow-up observations.
As part of the KEST, ESPRINT, and PICK2 collaborations (Cochran et al. 2015; Grziwa et al. 2015; SanchisOjeda et al. 2015; Johnson et al. 2016; Nespral et al.
2016), we have recently started a RV follow-up program
that aims at confirming Neptune-sized candidates detected by the K2 mission and at measuring their masses
via high-precision RV follow-up observations. We herein
report the discovery of K2-98 b (EPIC 211391664 b), a
transiting Neptune-sized planet in a 10-day orbit around
a relatively bright (V=12.2 mag) solar-like star photometrically monitored by the K2 mission during its Campaign 5. We combine the K2 photometry with groundbased follow-up observations to assess the planetary nature of the transiting object and derive its mass. We
note that K2-98 b has been recently identified as a planet
candidate by Pope et al. (2016) and Barros et al. (2016),
but has not previously been confirmed. We are the first
team to confirm and characterize in detail this planetary
system.
The paper is organized as follows: in Sect. 2 we present
the K2 photometry, and in Sect. 3 and 4 our groundbased photometric and spectroscopic follow-up, respectively. Sect. 5 reports on the characterization of the
host star. Sect. 6 describes the joint RV and photometric analysis. Results, discussion, and conclusion are
given in Sect. 7 and 8.
2. K2 LIGHT CURVE
K2 Campaign 5 observations began on 27 April
2015 UT and lasted until 10 July 2015 UT2 . During the observations the boresight of the Kepler
spacecraft was pointed at coordinates α = 08h 40m 38s ,
δ = +16◦ 49 0 47 00 . A total of 26 054 light curves were simultaneously acquired by K2; 25 850 in long cadence
mode (∼30 minute integration time) and 204 in short
cadence mode (∼1 minute integration time).
In this work, we use the light curves extracted by Vanderburg & Johnson (2014)3 . They were the only publicly available light curves at the time we started the
detection of transiting planet candidates in K2 Field 5.
We search the light curves for transit signals using the
DST algorithm (Cabrera et al. 2012) and the EXOTRANS
pipeline (Grziwa et al. 2012). DST and EXOTRANS have
been applied extensively to both CoRoT (Carpano et al.
2009; Cabrera et al. 2009; Erikson et al. 2012; Carone
et al. 2012; Cavarroc et al. 2012) and Kepler (Cabrera
et al. 2014; Grziwa & Pätzold 2016) data. All transit
detection algorithms search for a pattern in the data
and use statistics to assess whether a signal is present
in the data or not. When compared to widely used algorithms such as, e.g., Box Least Squares (BLS; Kovács
et al. 2002), DST uses an optimized transit shape, with
the same number of free parameters as BLS, and an optimized statistic for signal detection. EXOTRANS uses a
combination of the wavelet based filter technique VARLET
(Grziwa & Pätzold 2016) and the BLS detection algorithm. VARLET was developed to reduce both stellar
variability and data discontinuities. EXOTRANS calculates the Signal Detection Efficiency (SDE) for every
light curve when the BLS algorithm is used. The Generalized Extreme Value (GEV) distribution is used to
calculate the SDE threshold (Grziwa et al. 2012). We
consider all light curves with a SDE value higher than
the SDE threshold for further inspection (about 4 % of
the sample).
Both DST and EXOTRANS identify a periodic transitlike signal associated with the target EPIC 211391664.
The star was proposed for K2 observations by programs
GO5007 (P.I.: J. Winn) and GO5029 (P.I.: D. Charbonneau). For brevity we will hereafter refer to the star and
its transiting planet as K2-98 and K2-98 b, respectively.
The target passes all of the tests that we carry out to
2
1
As of June 2016; source: exoplanet.org.
3
See http://keplerscience.arc.nasa.gov/k2-fields.html.
Publicly available at
~avanderb/allk2c5obs.html.
https://www.cfa.harvard.edu/
3
The Neptune-sized planet K2-98 b
identify likely false positives with the DST and EXOTRANS
pipelines. These tests were regularly used during the
CoRoT mission. Briefly, we stack and fit even and odd
transits separately using the Transit Analysis package
TAP (Gazak et al. 2012). We find neither significant
odd-even transit depth variations, nor ellipsoidal variability/tidal deformation signatures in the light curve,
both typically observed in eclipsing binaries. We find
also no shallow secondary eclipses that might suggest
an eclipsing binary scenario. Possible secondary eclipses
are simulated using the detached eclipsing binary light
curve fitter (DEBIL; Devor 2005) we first described in
Pätzold et al. (2012). Similar tests are performed using the DST pipeline and are described in Cabrera et al.
(2009) and Cabrera et al. (2012). Large photometric
variation in phase with the candidate orbital period is
a hint for a possible binary. Such variations are also
not found, and so we proceed to more detailed fitting of
the light curve, as well as high-resolution imaging, reconnaissance spectroscopy, and RV observations (Sect. 3
and 4).
We also search the K2 light curve of K2-98 for additional transit signals, but none are found. The main
identifiers, optical and infrared magnitudes, and proper
motions of this star are listed in Table 2.
3. FASTACAM HIGH-RESOLUTION IMAGING
We observed K2-98 on 17 May 2016 with the FASTCAM lucky imaging camera (Oscoz et al. 2008) mounted
on the 1.5m Carlos Sánchez Telescope of Teide Observatory in Tenerife (Spain). To account for the low altitude of the object at the time of our observation, we
used a relatively long exposure time of 300 milliseconds
and acquired a total of 5 000 images. The integration
time of 300 milliseconds does not completely freeze the
atmosphere, but this duration was necessary to collect
enough light to detect faint objects. We selected the 300
best images, i.e., those with the highest Strehl ratio, and
processed the data using the COELI4 algorithm (Cagigal
et al. 2016a). COELI provides a map of the temporal
covariance between the intensity of K2-98 and the intensity of the remaining pixels (Fig. 1). This removes
the speckled halo surrounding the host star and creates
a dark ring-shaped region around it, which is the zone
were the algorithm is more sensitive to the presence of
faint objects (Cagigal et al. 2016b). COELI also reinforces in this zone those pixels whose intensity follows
the same temporal fluctuations as K2-98, which can only
happen when the pixels contain an object. We estimate
that in the ring-shaped region, at distances of 0.5–1.700 ,
4 ImageJ Plugin available at https://imagej.nih.gov/ij/
plugins/index.html.
Table 1. Main identifiers, magnitudes, and proper motion
of K2-98.
Parameter
Value
Source
211391664
EPIC
UCAC
508-047859
EPIC
2MASS
08255719+1130402
Main Identifiers
EPIC
h
m
EPIC
α(J2000.0)
s
08 05 57.189
EPIC
δ(J2000.0)
+11◦ 300 40.1200
EPIC
B
12.646±0.030
EPIC
V
12.166±0.030
EPIC
g
12.313±0.030
EPIC
r
12.031±0.030
EPIC
J
11.124±0.022
2MASS
H
10.905±0.025
2MASS
K
10.869±0.028
2MASS
W1
10.823±0.023
WISE
W2
10.856±0.020
WISE
W3
10.678±0.108
WISE
W4
8.258
WISE
−15.4 ± 2.3
UCAC2
−8.8 ± 1.5
UCAC2
Magnitudes
Proper motions
µα cos δ (mas yr−1 )
µδ (mas yr
−1
)
Note—Values of fields marked with EPIC are taken from the Ecliptic
Plane Input Catalog, available at http://archive.stsci.edu/k2/epic/
search.php. Values marked with UCAC2, 2MASS, and WISE are from
Zacharias et al. (2004), Cutri et al. (2003), Cutri & et al. (2013),
respectively. The WISE W 4 magnitude is an upper limit.
there are no background objects brighter than V≈19
mag (i.e., ∆V≈7 mag).
The final image shows the target to be isolated except
for the detection of an object located 1.900 South-East of
K2-98. The detected object is located just outside the
dark ring-shaped region, in a zone where COELI provides
relatively poor contrast and small spots show arbitrarily amplified noise. Nevertheless, due to being rather
bright, we consider the source as a secure detection, and
estimate it to be 50±10 times fainter (4.2±0.2 mag) than
the main target. The distance of 1.900 between the target and the faint object is less than the sky-projected
size of the Kepler/K2 CCD pixel (∼400 ). We therefore
assume that the light from the faint object contributes
with a fraction of 1/(50±10) to the measured flux of
K2-98 and correct the K2 light curve accordingly prior
to performing the joint analysis presented in Sect.6.
No additional contaminants are identified. The DSS
images reveal that the next closest star with a brightness
comparable to the target is a ∼3.5-mag fainter object
4
Barragán et al.
Table 2. Radial velocity measurements of K2-98.
BJDTDB
RV
σRV
CCF FWHM
CCF BIS
(km s−1 )
(km s−1 )
(km s−1 )
(km s−1 )
7342.706590
76.6027
0.0082
15.1659
0.0390
7344.744082
76.6243
0.0081
15.1694
0.0401
7347.706247
76.6143
0.0082
15.1770
0.0430
7394.699773
76.6130
0.0082
15.1790
0.0366
7509.495449
76.7558
0.0084
10.3567
0.0430
7511.495428
76.7516
0.0053
10.3617
0.0442
7512.472984
76.7376
0.0055
10.3632
0.0450
7516.525371
76.7425
0.0068
10.3729
0.0600
7371.582060
76.7393
0.0077
10.3474
0.0407
7371.601679
76.7324
0.0098
10.3309
0.0499
7448.440479
76.7499
0.0074
10.3352
0.0456
7512.429111
76.7313
0.0048
10.3558
0.0580
−2 450 000
FIES
HARPS
Figure 1. FASTCAM image of K2-98 processed with COELI.
The pixel scale is 0.04200 ; North is left, East is down. K2-98 is
at the center of the ring-shaped feature, which is an artifact
of the image processing. The faint nearby star 1.900 SouthEast of K2-98 is indicated with a green arrow. Colors from
blue to red represent the increasing level of temporal covariance with the central target, following the data processing
with COELI.
that is located at ∼4200 East of K2-98, which is too large
to produce any relevant influence onto the K2 light curve
of K2-98.
4. SPECTROSCOPIC FOLLOW-UP
OBSERVATIONS
We took 2 reconnaissance spectra of K2-98 with the
Harlan J. Smith 2.7m Telescope and the Tull Coudé
Spectrograph (Tull et al. 1995) at McDonald Observatory. The Tull spectrograph covers the entire optical spectrum (3450–9800 Å) at a resolving power of
R≈60 000. We used exposure times of 1800 seconds,
which resulted in a signal-to-noise ratio (SNR) of ∼ 30
per pixel at 5500 Å. We derived a first estimate of the
spectroscopic parameters by using our code Kea that
compares observed high-resolution spectra to a large library of synthetic models (Endl & Cochran 2016). For
the first spectrum we obtain the following parameters:
Teff = 5880 ± 107 K, log g? = 3.81 ± 0.31 (cgs), [Fe/H] =
−0.06 ± 0.07 dex and a v sin i? = 8.8 ± 0.3 km s−1 . For
the second observation: Teff = 5820 ± 116 K, [Fe/H] =
−0.03 ± 0.08 dex, log g? = 4.00 ± 0.35 (cgs) and a
v sin i? = 8.7 ± 0.4 km s−1 . We also measure an absolute
RV of 76.7 ± 0.2 km s−1 by cross-correlating the data
with spectra of the RV standard star HD 50692 (Udry
et al. 1999).
We also acquired 4 high-resolution spectra (R≈67 000)
in November 2015 and January 2016 using the FIbre-fed
Échelle Spectrograph (FIES; Frandsen & Lindberg 1999;
Telting et al. 2014) mounted at the 2.56m Nordic Optical Telescope (NOT) at Roque de los Muchachos Observatory (La Palma, Spain). We adopted the observing
strategy described in Buchhave et al. (2010) and Gan-
HARPS-N
dolfi et al. (2013, 2015), i.e., we took 3 consecutive exposures of 1200 seconds per observation epoch – to remove
cosmic ray hits – and acquired long-exposed (Texp ≈35
seconds) ThAr spectra immediately before and after the
three sub-exposures – to trace the RV drift of the instrument. We reduced the data using standard IRAF
and IDL routines. The signal-to-noise ratio (SNR) of
the extracted spectra is ∼30 per pixel at 5500 Å. Radial velocity measurements were derived via multi-order
cross-correlation with the RV standard star HD 50692
– observed with the same instrument set-up as K2-98.
They are listed in Table 2 along with the full-width at
half maximum (FWHM) and bisector span (BIS) of the
cross-correlation function (CCF).
We also acquired 8 high resolution spectra using the
HARPS (R≈115 000; Mayor et al. 2003) and HARPSN spectrographs (R≈115 000; Cosentino et al. 2012)
mounted at the ESO-3.6m telescope at La Silla observatory (Chile) and the 3.58m Telescopio Nazionale Galileo
(TNG) at the Roque de los Muchachos Observatory (La
Palma, Spain), respectively. The observations were performed between December 2015 and May 2016, setting
the exposure times to 1800–3600 seconds depending on
the sky condition. We monitored the Moon background
light using the second fiber and reduced the data with
the dedicated HARPS and HARPS-N data reduction
software pipeline. The SNR of the extracted spectra
is SNR=35–45 per pixel at 5500 Å. Radial velocities
(Table 2) were extracted by cross-correlation with a G2
numerical mask (Baranne et al. 1996; Pepe et al. 2002).
We search for possible correlations between the RVs
The Neptune-sized planet K2-98 b
and the CCF FWHM, as well as between the RVs and
CCF BIS. By combining all the three data sets, we derive for the RV and BIS data a Pearson correlation coefficient of -0.36 with a p-value of 0.25, while for the RV
and FWHM measurements we obtain a Pearson correlation coefficient of -0.32 with a p-value of 0.31. The lack
of significant correlations at a 0.05 confidence level provides further evidence that the observed RV variations
are caused by the orbital motion of the planet rather
than stellar activity. It also excludes the presence of an
unseen stellar contaminant whose CCF is blended with
the cross-correlation function of K2-98. We also perform a visual inspection of the Tull, FIES, HARPS, and
HARPS-N spectra and search the CCFs for the presence
of a secondary peak. We find no significant evidence of
a second set of spectral lines in the data.
5. PROPERTIES OF THE HOST STAR
We co-add the spectra from the NOT, ESO-3.6m, and
TNG separately to get a combined FIES spectrum, a
separate combined HARPS spectrum, and a third separate HARPS-N spectrum. The co-added data have a
SNR of ∼100 per pixel at 5500 Å. We use the three
combined spectra to refine the estimates of the spectroscopic parameters of the host star. Following the
spectral analysis of CoRoT and Kepler host stars (e.g.,
Fridlund et al. 2010; Gandolfi et al. 2010, 2015), we select spectral features that are sensitive to different photospheric parameters. Our method is based on Spectroscopy Made Easy (SME), a software package that calculates synthetic spectra and fits them to high resolution
observed spectra (Valenti & Piskunov 1996). SME is especially designed to determine basic stellar and atomic
parameters from a match of the observed and normalized spectrum to the synthetic spectra generated from
the parameterized atmospheres. It uses a non-linear
least squares algorithm to solve for any subset of allowed
parameters, which include atomic data (log gf and van
der Waals damping constants), the model atmosphere
parameters (Teff , log g? ), the metal abundances, and
the projected rotational velocity v sin i? . The SME 4.43
distribution includes a grid with a very large set of
1D-LTE plane-parallel stellar atmospheric models (ATLAS9, ATLAS12, NextGen, and MARCS models; Kurucz 1993, 2013; Hauschildt et al. 1999; Gustafsson et
al. 2008). ATLAS12 is an opacity sampling model atmosphere program that computes the same models as
ATLAS9 but instead of using pretabulated opacities and
models with arbitrary abundances, ATLAS12 uses individual abundances and line data.
Our spectral analysis begins by primarily using the
wings of the Hα and Hβ Balmer lines to determine
Teff , adopting the calibration equations of Bruntt et al.
(2010) and Doyle et al. (2014) to estimate the micro-
5
turbulent (Vmic ) and macroturbulent (Vmac ) velocities.
The projected rotational velocity v sin i? is determined
from a set of iron lines after which Mg i lines at λ = 5167,
5173, and 5184 Å and Ca i lines at λ = 6102, 6122, 6162,
and 6439 Å, are used to estimate the surface gravity
log g? . In order to verify the accuracy of this method,
we analyze a Solar spectrum from Wallace et al. (2011).
Comparing with the discussion given in Valenti & Fischer (2005), we find the errors quoted there to be representative of what can currently be achieved when calculating synthetic spectra in order to fit high resolution,
high SNR spectra.
We obtain stellar parameters from the FIES, HARPS,
HARPS-N consistent to within 1-sigma uncertainties.
Our final adopted values for Teff , log g? , [M/H], and
v sin i? are the weighted means of the values produced
by the three co-added spectra and the quoted errors are
the 1-σ standard deviation. They are also consistent
within 2-σ with the preliminary values derived from the
2 reconnaissance spectra taken at McDonald observatory (Sect. 4). We note that the v sin i? estimates obtained from the Tull spectroscopic data using KEA should
be regarded as upper limits as they do not account for
the line broadening induced by the macroturbulent velocity (Endl & Cochran 2016).
We determine stellar mass, radius, and age by combining the effective temperature Teff and metallicity [M/H]
with the mean density ρ? obtained from the transit light
curve modeling (Sect. 6). We compare the position of
the host star on a ρ? -versus-Teff with a fine grid of evolutionary tracks. The latter are computed ad hoc for this
work using the FRANEC code (Tognelli et al. 2011), setting the same configuration as for the Pisa stellar evolution data base for low-mass stars5 (Dell’Omodarme
et al. 2012). We adopt the mixing-length parameter
αml =1.74, which is our solar calibrated value for the
heavy element mixture of the Sun by Asplund et al.
(2009). We account for microscopic diffusion by means
of the routine developed by Thoul et al. (1994). The final grid contains tracks in the mass range 0.90-1.30 M ,
with a step of 0.01 M , computed for five different couples of initial metallicity Z and helium abundance Y ,
namely, (0.006, 0.260), (0.008, 0.265), (0.010, 0.268),
(0.011, 0.271), (0.012, 0.273), and (0.013, 0.274). We
find that evolutionary models with initial metal content
between Z=0.011 and Z=0.013 reproduce the current
photospheric metallicity. With a mass of M? =1.074 ±
0.042 M , radius of R? =1.311+0.083
−0.048 R and an age of
+1.2
5.2−1.0 Gyr (Table 3), K2-98 is a slightly evolved star
leaving the main sequence. Based on the calibration of
5
Available at http://astro.df.unipi.it/stellar-models/.
6
Barragán et al.
Straizys & Kuriliene (1981) for dwarf stars, the effective
temperature of the star translates into a F8 V spectral
type. The stellar mass and radius imply a surface grav+0.03
ity of log g? = 4.23−0.05
(cgs), which agrees within 1-σ
with the value of log g? = 4.35 ± 0.10 (cgs) derived from
the co-added spectra.
We check the K2 data for evidence of rotational
modulation.
The lack of significant periodic and
quasi-periodic photometric variation prevents us from
estimating the stellar rotation period.
Assuming
that the star is seen equator-on, the projected rotational velocity v sin i? =6.1±0.5 km s−1 and stellar radius R? =1.311+0.083
−0.048 R imply a rotational period of
+1.0
Prot =10.9−0.8 days.
Following the technique described in Gandolfi et al.
(2008), we use the magnitudes listed in Table 2 and
our spectroscopic parameters to estimate the interstellar extinction and distance to the star. We find
that the light of K2-98 suffers a negligible reddening
(Av =0.05±0.05 mag) and the star is located at a distance d = 435+40
−20 pc from the Sun.
6. JOINT RV-TRANSIT MODELING
We perform the joint modeling of the photometric and spectroscopic data using the code pyaneti, a
Python/Fortran software suite that finds the best fitting solution using Markov Chain Monte Carlo (MCMC)
methods based on Bayesian inference (Barragán et al., in
preparation). The code implements ensemble sampling
with affine invariance for a larger coverage of parameter
space (Goodman & Weare 2010).
The photometric data included in the joint analysis are subsets of the whole K2 light curve. We select ∼13 hours of data-points centered on each of the
7 transits6 observed by K2. We de-trend the individual
transits using a second-order polynomial locally fitted
to the ∼16 out-of-transit points per transit (8 points
per side). The final data-set contains 180 photometric
points. The modeled RV data-set contains the 12 measurements listed in Table 2.
The radial velocity model is given by a Keplerian orbit and an offset term for each systemic velocity (see,
e.g., Perryman 2014). We fit for the systemic velocity
γj (as measured by the j th instrument), the RV semiamplitude variation K, the transit epoch T0 , the period
Porb , the eccentricity e, and the argument of periastron
of the star’s orbit ω measured from the ascending node
to its periastron.
The transit model follows the quadratic limb-darkened
law of Mandel & Agol (2002). We account for the
K2 long integration (Texp =29.425 minutes) by supers-
6
The transit duration is ∼5 hours.
ampling the transit model with 10 sub-samples per long
cadence data (Kipping 2010). For the linear u1 and
quadratic u2 limb darkening coefficients, we use the
q1 = (u1 + u2 )2 and q2 = u1 [ 2 (u1 + u2 ) ]−1 parameterization described in Kipping (2013). The fitted transit
parameters are T0 , Porb , e, ω, q1 , q2 , scaled semi-major
axis a/R? , planet-to-star radius ratio Rp /R? , and impact parameter b.
We use the Gaussian likelihood
"
−n/2
L = (2π)
n
Y
i=1
#
"
σi exp −
n
X
(Di − Mi )2
i=1
2σi2
#
,
(1)
where n = ntr + nRV is the number of transit and RV
points, and σi is the error associated to each data point
Di , and Mi is the model associated to a given Di .
We fit for both a circular and an eccentric
model.
The joint modeling is carried out running 500 independent chains with uninformative uniform priors in the wide ranges Porb = [10.1, 10.2] days,
T0 = [2457145.7, 2457146.3], b = [0, 1], a/R? = [5, 100],
Rp /R? = [0.005, 0.2], K = [0.001, 1.0] km s−1 , and γj =
[1, 100] km s−1 . For the circular model we set e = 0
and ω = 90 deg, while for the eccentric fit we set uniformative uniform priors between the limits e = [0, 1] and
ω = [0, 360] deg. For q1 and q2 we set uniformative uniform priors in the range [0, 1] to sample a physical solution for the limb darkening coefficients (Kipping 2013).
We check the chain convergence by comparing the
“between-chain” and “within-chain” variance using the
Gelman-Rubin statistics. The burning-in phase used
25 000 additional iterations with a thin factor of 50, leading to a final number of 500 independent points for each
chain, i.e., 250 000 independent points for each fitted
parameter.
An initial global fit to the data yields the parameterized limb darkening coefficients q1 =0.27+0.29
−0.12 and
+0.26
q2 =0.47−0.24 which corresponds to u1 = 0.47+0.14
−0.17
and u2 = 0.03+0.36
−0.21 . As described in Csizmadia et
al. (2013), the large uncertainties arise from the shallow transit depth (∼0.1 %), the small number of data
points (∼180) and transits (7), and the K2 long integration time (∼30 minutes). We thus choose to constrain the limb darkening coefficient interpolating the
table of Claret & Bloemen (2011) and assuming conservative 20 % error bars. We stress that the system parameters derived with uninformative priors on the limb
darkening coefficients are consistent to within 1-σ uncertainties with those obtained by constraining u1 and u2 .
7. RESULTS AND DISCUSSION
Figure 2 shows the folded transit light curves and
phase-folded RV curve, along with their best fitting
models. The parameter estimates and error bars are
7
1.0005
0.9995
0.9990
0.9985
0.0003
0.0000
0.0003
0.0006
25
FIES
20
HARPS-N
15
HARPS
10
5
0
5
10
15
20
6.25
2.50
11.25
20.00
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
RV (m/s)
1.0000
3
2
1
0
1
T - T0 (hours)
2
3
Residuals (m/s)
Residuals
Relative flux
The Neptune-sized planet K2-98 b
Orbital phase
Figure 2. Left panel : Transit light curve folded to the orbital period of K2-98 b and residuals. The red points are the K2 data
and their error bars. The solid line mark the re-binned best fitting transit model. Right panel : Phase-folded FIES (blue circles),
HARPS-N (green diamonds) and HARPS (red triangles) RV measurements of K2-98 and best fitting circular orbit (solid line),
following the subtraction of the systemic velocities as measured from each instrument.
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
10
Radius (R⊕ )
listed in Table 3. They are taken as the median and
the 68 % central interval of the final posterior distributions (Gregory 2010). Our results are consistent with
the transit parameters derived by Pope et al. (2016) and
Barros et al. (2016).
Our RV measurements do not allow us to constrain
the eccentricity of the system. A fit for an eccentric orbit yields 0.19+0.17
−0.13 with a significance of only about 1-σ.
In order to further check whether the non-zero eccentricity solution is significant or not, we run an F-test and
calculate the p-value, i.e., the probability that the apparent eccentricity could have arisen if the underlying
orbit were circular (Lucy & Sweeney 1971). In doing
so we take into account the number of fitted parameters – both for the circular and eccentric model –, the
number of measurements and their uncertainties, and
the residuals from the best fitting circular and eccentric solution. We find a p-value of 0.87, which is much
higher than the 0.05 significance threshold suggested by
Lucy & Sweeney (1971) to prefer e 6= 0 over e = 0. We
therefore conclude that the nonzero best fitting eccentricity obtained with models where e is allowed to vary
is not significant. Moreover, we find that the circular
(DOF=153) and eccentric (DOF=151) models provide
very similar minimum χ2 values of ∼152. The difference
of the Bayesian information criterion is ∆BIC=10 between the two models, implying that the circular model
is favored. We therefore adopt the circular model as the
one that better describes our data. We note that the derived system parameters for a non-zero eccentricity are
consistent to within 1-σ uncertainties with those derived
assuming a circular orbit.
K2-98 b has a mass of Mp = 32.2 ± 8.1 M⊕ and a
+0.3
radius of Rp = 4.3−0.2
R⊕ , consistent with a density
−3
of 2.15+0.67
. These parameters are calculated
−0.60 g cm
adopting the stellar mass and radius derived in Sect. 5
30
50
Mass (M⊕ )
70 90 110130
Figure 3.
Mass-radius diagram for Neptune-sized planets
(2.0 . Rp . 6.0 R⊕ ) whose both mass and radius have been
determined with a precision of at least ∼25 % (Exoplanet
Orbit Database, as of June 2016; Han et al. 2014). The red
circle marks the position of K2-98 b. The green diamond
and blue square show the position of Neptune and Uranus,
respectively. The solid and dashed lines mark the Earth
(5.5 g cm−3 ) and Neptune (1.6 g cm−3 ) isodensity curves.
and listed in Table 3. Figure 3 shows the position of K298 b in the mass-radius diagram for Neptune-sized planets. The plot includes only those objects whose both
mass and radius have been estimated with a precision
of at least ∼25 %. K2-98 b joins the family of intermediate mass (20<Mp <50 M⊕ ) Neptune-sized planets.
Whereas its radius is slightly larger than that of Neptune
(3.9 R⊕ ), the mass of K2-98 b is almost twice as large as
the mass of Neptune. This implies that a solid massive
core surrounded by a large atmosphere is expected (see,
e.g., Weiss & Marcy 2014).
Assuming a minimum mass solar nebula (MMSN), the
isolation mass (Schlichting 2014) of a planet at 0.093
AU is ∼0.004 M⊕ , which is significantly lower than the
mass of K2-98 b. In order to form K2-98 b in situ, a disk
8
Barragán et al.
surface density ∼5500 times larger than the MMSN is
required. This value would generate gravitational instabilities in the disk, because its Toomre parameter would
be Q ≈ 0.03 1 (Schlichting 2014). This scenario does
not support the in situ formation of K2-98 b.
Valsecchi et al. (2014) proposed that Neptune-mass
planets may form via migration of hot Jupiters that
come so close to their host stars as to fill their Roche lobe
and start conservative mass transfer to the star. This
may reverse the direction of migration and increase the
orbital period. However, it seems very difficult to reach
a final orbital period of about 10 days, as in the case
of K2-98 b. Moreover, this formation scenario cannot
easily account for the measured relatively low density of
−3
the planet (2.15+0.67
). Therefore, we argue that
−0.60 g cm
K2-98 b likely formed in the outer region of the protoplanetary disk and then migrated inwards to its current
position (see, e.g. Kley & Nelson 2012).
We integrate the equations of tidal and rotational evolution as in Lanza & Mathis (2016) assuming a constant
modified tidal quality factor Q0? for the star. Given
that the stellar rotation period is close to the orbital period (Sect. 5), tidal dissipation by inertial waves inside
the star is considered leading to a remarkably stronger
tidal interaction than in the case of the equilibrium tide
(Ogilvie & Lin 2007). Therefore, we explore the evolution for three fixed values of Q0? , i.e., 105 , 106 , and
107 , from the stronger to the weaker coupling. Following Lanza et al. (2011), we include the loss of angular momentum produced by the stellar magnetized wind
considering a saturation regime for an angular velocity
greater than 8 Ω , where Ω is the present solar angular velocity. We assume that the orbit of the planet is
circular, although the tidal interaction is so weak that
any initial eccentricity could survive up to the present
stage of the system evolution (see below).
Fig. 4 shows the evolution of the rotation period of
the star (upper panel), semi-major axis of the planet’s
orbit (middle panel), and stellar radius (lower panel)
as obtained from the evolutionary models presented in
Sect. 5. Tidal interaction is so weak that there is virtually no evolution of the orbital separation since the
planet arrived at the present semi-major axis (Fig. 4,
middle panel). The rotation of the star is braked solely
by the stellar wind with a completely negligible tidal
exchange between the orbital and the spin angular momenta, and no dependency on the stellar tidal quality
factor Q0? , owing to the small mass of the planet and
large separation. (Fig. 4, upper panel). Under our model
assumptions, we estimate that the star reached the zero
age main sequence (ZAMS) with a rotation period of
about 1.5 days.
The tidal evolution of the planet will become important in the future – after ∼3 Gyr from now – due to
Figure 4. Rotational period of the star (upper panel), semi-
major axis of the planet orbit (middle-panel), and stellar
radius (lower panel) versus time. Different line styles refer to
different initial semi-major axis a0 and tidal quality factor of
the star Q0? as follows: solid line: Q0? = 106 , a0 = 0.0943 AU;
dotted line: Q0? = 107 , a0 = 0.0943 AU; dashed line: Q0? =
105 , a0 = 0.0943 AU; dash-dotted: Q0? = 105 , a0 = 0.037
AU (corresponding to an orbital period of 2.5 days); dashtriple-dotted: Q0? = 106 , a0 = 0.037 AU.
the increase of the stellar radius and rotational period
of the star, leading to a rapid decay of the planet’s orbit
(Fig. 4, middle panel).
The amount of angular momentum in the orbit is
insufficient to synchronize the rotation of the star, so
the present approximately synchronous state cannot be
maintained. Damiani & Lanza (2015) showed that other
systems having host stars with an effective temperature
around 6100 K show a rather wide distribution of the ratio of the orbital period to the stellar spin period, even
in the case of more massive planets, thus supporting the
conclusion that the present approximate synchronicity
is probably coincidental.
Finally, we consider the possibility that the planet was
initially significantly closer to the star when the latter
reached the ZAMS and was pushed outwards by the action of tides because angular momentum was transferred
from the stellar spin to the orbit, provided that the rotational period of the star was shorter than the orbital
one. We find that also this scenario is unlikely. As
an illustrative case, we show in Fig. 4 two integrations
The Neptune-sized planet K2-98 b
for the planet initially at an orbital period of 2.5 days,
corresponding to a semi-major axis of 0.037 AU. This
is the minimum orbital period for observed Neptunemass planets around main-sequence stars (cf. Fig. 4 of
Valsecchi et al. 2014) that we choose in order to maximize the strength of the tidal interaction. Since the star
was initially rotating faster than the planet, the tidal
interaction was initially pushing the planet outwards, in
particular for Q0? = 105 (Fig. 4, middle panel). However, the fast rotational braking of the star led soon to
a rotation period longer than the orbital period. Since
the amount of orbital angular momentum was too small
to maintain the synchronous state, the final fate of the
planet was to fall towards the star under the action of
tides within a few Gyrs7 . This scenario would account
for the significant dearth of Neptune-like planets with
orbital periods below 2-4 days (see, e.g., Szabó & Kiss
2011; Mazeh et al. 2016).
The tidal evolution of the system further supports an
inward migration scenario for K2-98 b, from the outer
region of the system to its current position.
8. CONCLUSIONS
We confirm the planetary nature of K2-98 b and
derive the system parameters. Our results are based on
photometric data from the K2 space mission combined
with high-precision Tull, FIES, HARPS, and HARPS-N
RV measurements and lucky imaging. K2-98 b is a transiting Neptune-sized planet in a 10-day-orbit around an
F8 V leaving the main sequence. It has a mass of Mp =
+0.3
32.2 ± 8.1 M⊕ and a radius of Rp = 4.3−0.2
R⊕ , trans−3
lating into a mean density of 2.15+0.67
. K2-98 b
−0.60 g cm
joins the still relatively small number of Neptune-size
planets (∼20 objects) whose mass and radius have been
determined with a precision better than 25 %.
We thank the anonymous referee for the insightful,
thoughtful and constructive review. We are very grateful to Simon Albrecht for providing us with one of
the HARPS-N measurement and for his valuable comments and suggestions. We are thankful to Jorge Melendez, Martin Kürster, François Bouchy, Nuno Santos, and Xavier Bonfils who kindly agreed to exchange
HARPS time with us. We express our deepest gratitude to the NOT, ESO, TNG and McDonald staff members for their unique support during the observations.
7 We note that assuming a different initial orbital period leads
to qualitatively similar scenarios. If the initial orbital period of the
planet is shorter than 2.5 days (i.e., a0 < 0.037 AU), tidal push is
stronger, but for a shorter time interval before the rotation period
of the star becomes longer than the orbital period, after which the
9
Szilard Csizmadia thanks the Hungarian OTKA Grant
K113117. Hans Deeg and David Nespral acknowledge
support by grant ESP2015-65712-C5-4-R of the Spanish Secretary of State for R& D&i (MINECO). This research was supported by the Ministerio de Economia y
Competitividad under project FIS2012-31079. The research leading to these results has received funding from
the European Union Seventh Framework Programme
(FP7/2013-2016) under grant agreement No. 312430
(OPTICON) and from the NASA K2 Guest Observer
Cycle 1 program under grant NNX15AV58G to The University of Texas at Austin. This paper includes data
taken at McDonald Observatory of the University of
Texas at Austin. Based on observations obtained a)
with the Nordic Optical Telescope (NOT), operated on
the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio
del Roque de los Muchachos (ORM) of the Instituto de
Astrofı́sica de Canarias (IAC); b) with the Italian Telescopio Nazionale Galileo (TNG) also operated at the
ORM (IAC) on the island of La Palma by the INAF Fundación Galileo Galilei. Based on observations made
with ESO Telescopes at the La Silla Observatory under
programme ID 097.C-0948. This research made use of
data acquired with the Carlos Sánchez (TCS) Telescope,
operated at Teide Observatory on the island of Tenerife
by the Instituto de Astrofı́sica de Canarias. This paper
includes data collected by the Kepler mission. Funding
for the Kepler mission is provided by the NASA Science Mission directorate. This publication makes use
of data products from the Two Micron All Sky Survey
(2MASS), which is a joint project of the University of
Massachusetts and the Infrared Processing and Analysis
Center/California Institute of Technology, funded by the
National Aeronautics and Space Administration and the
National Science Foundation. This publication makes
use of data products from the Wide-field Infrared Survey
Explorer (WISE), which is a joint project of the University of California, Los Angeles, and the Jet Propulsion
Laboratory/California Institute of Technology, funded
by the National Aeronautics and Space Administration.
Facilities: Kepler (K2), NOT (FIES), ESO:3.6m
(HARPS), Sanchez (FAST-CAM), Smith (Tull), TNG
(HARPS-N).
Software: COELI, DEBIL, DST, EXOTRANS, Kea IDL,
IRAF, pyaneti, SME, TAP.
orbit decays faster. If the planet is further out (P0,orb > 2.5 days
and a0 > 0.037 AU), tides are weaker, but they can act longer
before the direction of the evolution of the semi-major axis is
reversed and the planet falls into the star.
10
Barragán et al.
Table 3. Stellar and Planetary Parameters.
Parameter
Value
Model Parameters
Orbital period Porb (days)
10.13675 ± 0.00033
Transit epoch T0 (BJDTDB −2 450 000)
7145.9807 ± 0.0012
Scaled semi-major axis a/R?
15.388+0.543
−1.192
Scaled planet radius Rp /R?
0.0301+0.0004
−0.0003
0.27+0.17
−0.14
Impact parameter, b
a
0.40 ± 0.05
Parameterized limb-darkening coefficient q2 a
0.26 ± 0.05
Parameterized limb-darkening coefficient q1
Eccentricity e
0
Radial velocity semi-amplitude variation K (m s−1 )
9.1 ± 2.3
(fixed)
Systemic velocity γFIES (km s−1 )
76.6116 ± 0.0029
Systemic velocity γHARPS (km s−1 )
76.7479 ± 0.0022
Systemic velocity γHARPS−N (km s−1 )
76.7417 ± 0.0026
Derived parameters
Semi-major axis of the planetary orbit a (AU)
0.0943+0.0061
−0.0052
Transit duration τ14 (hours)
5.03+0.05
−0.04
Transit ingress/egress duration τ12 = τ34 (hours)
0.16+0.03
−0.01
Orbit inclination along the line-of-sight ip (◦ )
89.0+0.5
−0.7
Stellar parameters
1.074 ± 0.042
Star mass M? (M )
1.311+0.083
−0.048
Star radius R? (R )
Surface gravity log g? (cgs)
−3
Mean density ρ? (g cm
b
)
4.23+0.03
−0.05
0.66+0.07
−0.12
5.2+1.2
−1.0
Star age (Gyr)
Spectral typec
F8 V
Effective temperature Teff (K)
6120 ± 80
Iron abundance [Fe/H] (dex)
−0.2 ± 0.1
Nickel abundance [Ni/H] (dex)
−0.1 ± 0.1
Silicon abundance [Si/H] (dex)
−0.1 ± 0.1
Calcium abundance [Ca/H] (dex)
−0.1 ± 0.1
Sodium abundance [Na/H] (dex)
−0.0 ± 0.1
Magnesium abundance [Mg/H] (dex)
−0.0 ± 0.1
Microturbulent velocity vmic c
1.3 ± 0.1
Macroturbulent velocity vmac d
3.7 ± 0.6
Projected rotational velocity v sin i?
6.1 ± 0.5
435+40
−20
Distance d (pc)
Visual interstellar extinction Av (mag)
0.05 ± 0.05
Planetary parameters
32.2 ± 8.1
Planet mass Mp (M⊕ )
4.3+0.3
−0.2
Planet radius Rp (R⊕ )
−3
Planet density ρp (g cm
)
Equilibrium temperature Teq (K)
2.15+0.67
−0.60
1102+26
−20
Note—The adopted Sun and Earth units follow the recommendations from the International Astronomical Union (Prsa et al. 2016).
a The limb-darkening coefficient parameterization follows Kipping (2013). The estimates have been obtained assuming u = 0.33 ± 0.06 and
1
u2 = 0.30 ± 0.06 for the linear and quadratic limb-darkening coefficients (Claret & Bloemen 2011), adopting 20 % conservative error bars.
b Stellar surface gravity log g as measured from the global fit and evolutionary tracks. The spectroscopic analysis gives log g = 4.35 ± 0.10 (cgs).
?
?
c Based on the spectral type vs. effective temperature calibration of Straizys & Kuriliene (1981) for dwarf stars.
d Micro and macroturbulent velocities from the calibration equations of Bruntt et al. (2010) and Doyle et al. (2014), respectively.
The Neptune-sized planet K2-98 b
11
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